Fred the ant is on the real number line, and Fred is trying to get to the point 0.

If Fred is at 1 then on the next step, Fred moves to either 0 or 2 with equal probability.

If Fred is at 2 then on the next step, Fred always moves to 1.

Let e1 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 1.

Similarly, let e2 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 2

Determine the ordered pair (e1, e2)

Guest Aug 10, 2020